Convergence in $(\omega,m)$-capacity in the class $\mathcal{E}(X, \omega,m)$ on compact K\"ahler manifolds

Abstract

In this paper, we establish the weak*-convergence of a sequence of the complex Hessian measures $H_m(u_j)$ to the complex Hessian measure $H_m(u)$ in the class $\mathcal{E}(X,\omega,m)$ under hypotheses that $u_j$ is convergent to $u$ in $(\omega,m)$-capacity.